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Solvability Classes for Core Problems in Matrix Total Least Squares Minimization
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SYSNO ASEP 0504412 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Solvability Classes for Core Problems in Matrix Total Least Squares Minimization Author(s) Hnětynková, I. (CZ)
Plešinger, Martin (UIVT-O) RID, SAI, ORCID
Žáková, J. (CZ)Number of authors 3 Source Title Applications of Mathematics. - : Springer - ISSN 0862-7940
Roč. 64, č. 2 (2019), s. 103-128Number of pages 26 s. Language eng - English Country CZ - Czech Republic Keywords linear approximation problem ; core problem theory ; total least squares ; classification ; (ir)reducible problem Subject RIV BA - General Mathematics OECD category Applied mathematics Method of publishing Open access with time embargo (19.02.2021) Institutional support UIVT-O - RVO:67985807 UT WOS 000463984700002 EID SCOPUS 85064195522 DOI 10.21136/AM.2019.0252-18 Annotation Linear matrix approximation problems AX ≈ B are often solved by the total least squares minimization (TLS). Unfortunately, the TLS solution may not exist in general. The so-called core problem theory brought an insight into this effect. Moreover, it simplified the solvability analysis if B is of column rank one by extracting a core problem having always a unique TLS solution. However, if the rank of B is larger, the core problem may stay unsolvable in the TLS sense, as shown for the first time by Hnětynková, Plešinger, and Sima (2016). Full classification of core problems with respect to their solvability is still missing. Here we fill this gap. Then we concentrate on the so-called composed (or reducible) core problems that can be represented by a composition of several smaller core problems. We analyze how the solvability class of the components influences the solvability class of the composed problem. We also show on an example that the TLS solvability class of a core problem may be in some sense improved by its composition with a suitably chosen component. The existence of irreducible problems in various solvability classes is discussed. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2020 Electronic address http://hdl.handle.net/11104/0296053
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